/usr/include/fflas-ffpack/ffpack/ffpack_charpoly_danilevski.inl is in fflas-ffpack-common 1.6.0-1.
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// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s
/* ffpack/ffpack_charpoly_danilevski.inl
* Copyright (C) 2005 Clement Pernet
*
* Written by Clement Pernet <Clement.Pernet@imag.fr>
*
*
* ========LICENCE========
* This file is part of the library FFLAS-FFPACK.
*
* FFLAS-FFPACK is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
#ifndef MIN
#define MIN(a,b) (a<b)?a:b
#endif
namespace FFPACK {
//---------------------------------------------------------------------
// CharPoly: Compute the characteristic polynomial of A using
// Danilevski's algorithm.
//---------------------------------------------------------------------
template <class Field, class Polynomial>
std::list<Polynomial>&
Danilevski (const Field& F, std::list<Polynomial>& charp,
const size_t N, typename Field::Element * A,
const size_t lda)
{
charp.clear();
size_t dtot=0;
typename Field::Element *pivot,*e,*u1,invp;
for (size_t k=0; k<N; ++k){
size_t i = k+1;
size_t d;
e = pivot = A + (k+1) * lda + k; // coef
while ((i<N) && F.isZero(*e)) { e += lda; i++; }
if (i < N){
if (i > k + 1) {
FFLAS::fswap (F, N-k, e, 1, pivot, 1);
FFLAS::fswap (F, N, A+i, lda, A+k+1, lda);
}
F.inv (invp, *pivot);
FFLAS::fscal (F, N-k-1, invp, pivot+1, 1);
FFLAS::fscal (F, N-dtot, *pivot, A+dtot*lda+k+1, lda);
// X <- X - uw
FFLAS::fger (F, k + 1-dtot, N - k -1, F.mOne,
A + dtot*lda + k, lda, pivot+1, 1,
A+k+1+dtot*lda, lda);
if (k<N-2){
// Y <- Y - vw
FFLAS::fger (F, N-k-2, N-k-1, F.mOne, pivot+lda, lda, pivot+1, 1,
pivot+lda+1,lda);
//6
fgemv (F, FFLAS::FflasNoTrans, N-dtot, N-k-2,
F.one, A+dtot*lda+k+2, lda, pivot+lda, lda, F.one,
A+dtot*lda+k+1,lda);
}
//5
u1 = A+dtot*lda+k;
for (i = dtot; i <= k; ++i){
F.addin( *(u1+lda+1), *u1);
u1+=lda;
}
}
if (i==N){// completed one companion block
d = k+1-dtot;
typename Field::Element *Ai = A+k+dtot*lda;
Polynomial * P = new Polynomial(d+1);
for (i = 0; i < d; ++i){
F.neg (P->operator[](i), *(Ai+i*lda));
}
F.assign( (*P)[d], F.one);
charp.push_front(*P);
dtot+=d;
}
}
return charp;
}
} // FFPACK
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